A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by $v(t)=47\left[1-(0.87)^{t}\right]$ where $v(t)$ is measured in meters per second. What is her terminal velocity? Hint: Evaluate $\lim _{t \rightarrow \infty} v(t)$
A) 54 m/sec
B) 7 m/sec
C) 47 m/sec
D) 87 m/sec

Question

Quizplus · Accepted Answer

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, due to the balance of gravity and air resistance. When an object reaches its terminal velocity, its acceleration becomes zero.

To find the terminal velocity of the skydiver, we need to evaluate the limit of the velocity function as t goes to infinity:

$$\lim_{t	o\infty} v(t) = \lim_{t	o\infty} 47[1 - (0.87)^t]$$

Since the base of the exponential term is less than 1, we know that the term $(0.87)^t$ will approach zero as t increases without bound. Therefore:

$$\lim_{t	o\infty} 47[1 - (0.87)^t] = 47[1 - 0] = 47$$

This means that the skydiver will eventually reach a velocity of 47 m/sec and will no longer accelerate. Therefore, the best choice is C) 47 m/sec.

A Skydiver Leaps from a Helicopter Hovering High Above the Ground